
R version 4.0.3 (2020-10-10) -- "Bunny-Wunnies Freak Out"
Copyright (C) 2020 The R Foundation for Statistical Computing
Platform: x86_64-apple-darwin17.0 (64-bit)

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  Natural language support but running in an English locale

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> 
> #################This code generates figure 3,4 and 5####################
> library(RColorBrewer)
> library(latex2exp)
> 
> set.seed(213)
> 
> #################Use different n#################
> n_1 <- 100
> n_2 <- 1000
> n_3 <- 10000
> 
> 
> #################Setting up for different q*, upper bound for the conditional probability of M_ij being observed defined in assumption 2#################
> q_1 <- 0.75
> q_2 <- 0.9
> q_3 <- 0.99
> 
> 
> #################Compute probability of all missing and expected proportion of missing
> computation <- expand.grid(k = seq(1, 150, 1), n = c(n_1, n_2, n_3),
+             q = c(q_1,q_2,q_3))
> computation$p <- (1-computation$q^(computation$k))^(computation$n)
> computation$y <- 1-computation$q^(computation$k) # expected proportion of missing (does not depend on n)
> 
> computation
       k     n    q             p          y
1      1   100 0.75  6.223015e-61 0.25000000
2      2   100 0.75  1.252581e-36 0.43750000
3      3   100 0.75  1.592850e-24 0.57812500
4      4   100 0.75  3.018619e-17 0.68359375
5      5   100 0.75  1.718335e-12 0.76269531
6      6   100 0.75  3.078342e-09 0.82202148
7      7   100 0.75  5.993276e-07 0.86651611
8      8   100 0.75  2.623022e-05 0.89988708
9      9   100 0.75  4.075651e-04 0.92491531
10    10   100 0.75  3.039300e-03 0.94368649
11    11   100 0.75  1.336257e-02 0.95776486
12    12   100 0.75  3.999943e-02 0.96832365
13    13   100 0.75  9.031950e-02 0.97624274
14    14   100 0.75  1.656530e-01 0.98218205
15    15   100 0.75  2.604471e-01 0.98663654
16    16   100 0.75  3.651979e-01 0.98997740
17    17   100 0.75  4.702296e-01 0.99248305
18    18   100 0.75  5.681521e-01 0.99436229
19    19   100 0.75  6.546041e-01 0.99577172
20    20   100 0.75  7.278756e-01 0.99682879
21    21   100 0.75  7.881048e-01 0.99762159
22    22   100 0.75  8.364906e-01 0.99821619
23    23   100 0.75  8.746993e-01 0.99866214
24    24   100 0.75  9.044851e-01 0.99899661
25    25   100 0.75  9.274813e-01 0.99924746
26    26   100 0.75  9.451074e-01 0.99943559
27    27   100 0.75  9.585443e-01 0.99957669
28    28   100 0.75  9.687459e-01 0.99968252
29    29   100 0.75  9.764675e-01 0.99976189
30    30   100 0.75  9.822987e-01 0.99982142
31    31   100 0.75  9.866948e-01 0.99986606
32    32   100 0.75  9.900045e-01 0.99989955
33    33   100 0.75  9.924941e-01 0.99992466
34    34   100 0.75  9.943653e-01 0.99994350
35    35   100 0.75  9.957710e-01 0.99995762
36    36   100 0.75  9.968266e-01 0.99996822
37    37   100 0.75  9.976190e-01 0.99997616
38    38   100 0.75  9.982137e-01 0.99998212
39    39   100 0.75  9.986600e-01 0.99998659
40    40   100 0.75  9.989948e-01 0.99998994
41    41   100 0.75  9.992460e-01 0.99999246
42    42   100 0.75  9.994345e-01 0.99999434
43    43   100 0.75  9.995758e-01 0.99999576
44    44   100 0.75  9.996819e-01 0.99999682
45    45   100 0.75  9.997614e-01 0.99999761
46    46   100 0.75  9.998210e-01 0.99999821
47    47   100 0.75  9.998658e-01 0.99999866
48    48   100 0.75  9.998993e-01 0.99999899
49    49   100 0.75  9.999245e-01 0.99999924
50    50   100 0.75  9.999434e-01 0.99999943
51    51   100 0.75  9.999575e-01 0.99999958
52    52   100 0.75  9.999681e-01 0.99999968
53    53   100 0.75  9.999761e-01 0.99999976
54    54   100 0.75  9.999821e-01 0.99999982
55    55   100 0.75  9.999866e-01 0.99999987
56    56   100 0.75  9.999899e-01 0.99999990
57    57   100 0.75  9.999924e-01 0.99999992
58    58   100 0.75  9.999943e-01 0.99999994
59    59   100 0.75  9.999957e-01 0.99999996
60    60   100 0.75  9.999968e-01 0.99999997
61    61   100 0.75  9.999976e-01 0.99999998
62    62   100 0.75  9.999982e-01 0.99999998
63    63   100 0.75  9.999987e-01 0.99999999
64    64   100 0.75  9.999990e-01 0.99999999
65    65   100 0.75  9.999992e-01 0.99999999
66    66   100 0.75  9.999994e-01 0.99999999
67    67   100 0.75  9.999996e-01 1.00000000
68    68   100 0.75  9.999997e-01 1.00000000
69    69   100 0.75  9.999998e-01 1.00000000
70    70   100 0.75  9.999998e-01 1.00000000
71    71   100 0.75  9.999999e-01 1.00000000
72    72   100 0.75  9.999999e-01 1.00000000
73    73   100 0.75  9.999999e-01 1.00000000
74    74   100 0.75  9.999999e-01 1.00000000
75    75   100 0.75  1.000000e+00 1.00000000
76    76   100 0.75  1.000000e+00 1.00000000
77    77   100 0.75  1.000000e+00 1.00000000
78    78   100 0.75  1.000000e+00 1.00000000
79    79   100 0.75  1.000000e+00 1.00000000
80    80   100 0.75  1.000000e+00 1.00000000
81    81   100 0.75  1.000000e+00 1.00000000
82    82   100 0.75  1.000000e+00 1.00000000
83    83   100 0.75  1.000000e+00 1.00000000
84    84   100 0.75  1.000000e+00 1.00000000
85    85   100 0.75  1.000000e+00 1.00000000
86    86   100 0.75  1.000000e+00 1.00000000
87    87   100 0.75  1.000000e+00 1.00000000
88    88   100 0.75  1.000000e+00 1.00000000
89    89   100 0.75  1.000000e+00 1.00000000
90    90   100 0.75  1.000000e+00 1.00000000
91    91   100 0.75  1.000000e+00 1.00000000
92    92   100 0.75  1.000000e+00 1.00000000
93    93   100 0.75  1.000000e+00 1.00000000
94    94   100 0.75  1.000000e+00 1.00000000
95    95   100 0.75  1.000000e+00 1.00000000
96    96   100 0.75  1.000000e+00 1.00000000
97    97   100 0.75  1.000000e+00 1.00000000
98    98   100 0.75  1.000000e+00 1.00000000
99    99   100 0.75  1.000000e+00 1.00000000
100  100   100 0.75  1.000000e+00 1.00000000
101  101   100 0.75  1.000000e+00 1.00000000
102  102   100 0.75  1.000000e+00 1.00000000
103  103   100 0.75  1.000000e+00 1.00000000
104  104   100 0.75  1.000000e+00 1.00000000
105  105   100 0.75  1.000000e+00 1.00000000
106  106   100 0.75  1.000000e+00 1.00000000
107  107   100 0.75  1.000000e+00 1.00000000
108  108   100 0.75  1.000000e+00 1.00000000
109  109   100 0.75  1.000000e+00 1.00000000
110  110   100 0.75  1.000000e+00 1.00000000
111  111   100 0.75  1.000000e+00 1.00000000
112  112   100 0.75  1.000000e+00 1.00000000
113  113   100 0.75  1.000000e+00 1.00000000
114  114   100 0.75  1.000000e+00 1.00000000
115  115   100 0.75  1.000000e+00 1.00000000
116  116   100 0.75  1.000000e+00 1.00000000
117  117   100 0.75  1.000000e+00 1.00000000
118  118   100 0.75  1.000000e+00 1.00000000
119  119   100 0.75  1.000000e+00 1.00000000
120  120   100 0.75  1.000000e+00 1.00000000
121  121   100 0.75  1.000000e+00 1.00000000
122  122   100 0.75  1.000000e+00 1.00000000
123  123   100 0.75  1.000000e+00 1.00000000
124  124   100 0.75  1.000000e+00 1.00000000
125  125   100 0.75  1.000000e+00 1.00000000
126  126   100 0.75  1.000000e+00 1.00000000
127  127   100 0.75  1.000000e+00 1.00000000
128  128   100 0.75  1.000000e+00 1.00000000
129  129   100 0.75  1.000000e+00 1.00000000
130  130   100 0.75  1.000000e+00 1.00000000
131  131   100 0.75  1.000000e+00 1.00000000
132  132   100 0.75  1.000000e+00 1.00000000
133  133   100 0.75  1.000000e+00 1.00000000
134  134   100 0.75  1.000000e+00 1.00000000
135  135   100 0.75  1.000000e+00 1.00000000
136  136   100 0.75  1.000000e+00 1.00000000
137  137   100 0.75  1.000000e+00 1.00000000
138  138   100 0.75  1.000000e+00 1.00000000
139  139   100 0.75  1.000000e+00 1.00000000
140  140   100 0.75  1.000000e+00 1.00000000
141  141   100 0.75  1.000000e+00 1.00000000
142  142   100 0.75  1.000000e+00 1.00000000
143  143   100 0.75  1.000000e+00 1.00000000
144  144   100 0.75  1.000000e+00 1.00000000
145  145   100 0.75  1.000000e+00 1.00000000
146  146   100 0.75  1.000000e+00 1.00000000
147  147   100 0.75  1.000000e+00 1.00000000
148  148   100 0.75  1.000000e+00 1.00000000
149  149   100 0.75  1.000000e+00 1.00000000
150  150   100 0.75  1.000000e+00 1.00000000
151    1  1000 0.75  0.000000e+00 0.25000000
152    2  1000 0.75  0.000000e+00 0.43750000
153    3  1000 0.75 1.051357e-238 0.57812500
154    4  1000 0.75 6.281789e-166 0.68359375
155    5  1000 0.75 2.244281e-118 0.76269531
156    6  1000 0.75  7.641321e-86 0.82202148
157    7  1000 0.75  5.979199e-63 0.86651611
158    8  1000 0.75  1.541768e-46 0.89988708
159    9  1000 0.75  1.264649e-34 0.92491531
160   10  1000 0.75  6.725669e-26 0.94368649
161   11  1000 0.75  1.815101e-19 0.95776486
162   12  1000 0.75  1.048427e-14 0.96832365
163   13  1000 0.75  3.612563e-11 0.97624274
164   14  1000 0.75  1.555943e-08 0.98218205
165   15  1000 0.75  1.436134e-06 0.98663654
166   16  1000 0.75  4.219706e-05 0.98997740
167   17  1000 0.75  5.285668e-04 0.99248305
168   18  1000 0.75  3.504659e-03 0.99436229
169   19  1000 0.75  1.444731e-02 0.99577172
170   20  1000 0.75  4.174186e-02 0.99682879
171   21  1000 0.75  9.243571e-02 0.99762159
172   22  1000 0.75  1.677300e-01 0.99821619
173   23  1000 0.75  2.621730e-01 0.99866214
174   24  1000 0.75  3.664493e-01 0.99899661
175   25  1000 0.75  4.710332e-01 0.99924746
176   26  1000 0.75  5.686063e-01 0.99943559
177   27  1000 0.75  6.548197e-01 0.99957669
178   28  1000 0.75  7.279451e-01 0.99968252
179   29  1000 0.75  7.880941e-01 0.99976189
180   30  1000 0.75  8.364420e-01 0.99982142
181   31  1000 0.75  8.746377e-01 0.99986606
182   32  1000 0.75  9.044236e-01 0.99989955
183   33  1000 0.75  9.274261e-01 0.99992466
184   34  1000 0.75  9.450607e-01 0.99994350
185   35  1000 0.75  9.585062e-01 0.99995762
186   36  1000 0.75  9.687155e-01 0.99996822
187   37  1000 0.75  9.764438e-01 0.99997616
188   38  1000 0.75  9.822803e-01 0.99998212
189   39  1000 0.75  9.866806e-01 0.99998659
190   40  1000 0.75  9.899938e-01 0.99998994
191   41  1000 0.75  9.924859e-01 0.99999246
192   42  1000 0.75  9.943591e-01 0.99999434
193   43  1000 0.75  9.957664e-01 0.99999576
194   44  1000 0.75  9.968231e-01 0.99999682
195   45  1000 0.75  9.976164e-01 0.99999761
196   46  1000 0.75  9.982117e-01 0.99999821
197   47  1000 0.75  9.986585e-01 0.99999866
198   48  1000 0.75  9.989937e-01 0.99999899
199   49  1000 0.75  9.992452e-01 0.99999924
200   50  1000 0.75  9.994338e-01 0.99999943
201   51  1000 0.75  9.995753e-01 0.99999958
202   52  1000 0.75  9.996815e-01 0.99999968
203   53  1000 0.75  9.997611e-01 0.99999976
204   54  1000 0.75  9.998208e-01 0.99999982
205   55  1000 0.75  9.998656e-01 0.99999987
206   56  1000 0.75  9.998992e-01 0.99999990
207   57  1000 0.75  9.999244e-01 0.99999992
208   58  1000 0.75  9.999433e-01 0.99999994
209   59  1000 0.75  9.999575e-01 0.99999996
210   60  1000 0.75  9.999681e-01 0.99999997
211   61  1000 0.75  9.999761e-01 0.99999998
212   62  1000 0.75  9.999821e-01 0.99999998
213   63  1000 0.75  9.999865e-01 0.99999999
214   64  1000 0.75  9.999899e-01 0.99999999
215   65  1000 0.75  9.999924e-01 0.99999999
216   66  1000 0.75  9.999943e-01 0.99999999
217   67  1000 0.75  9.999957e-01 1.00000000
218   68  1000 0.75  9.999968e-01 1.00000000
219   69  1000 0.75  9.999976e-01 1.00000000
220   70  1000 0.75  9.999982e-01 1.00000000
221   71  1000 0.75  9.999987e-01 1.00000000
222   72  1000 0.75  9.999990e-01 1.00000000
223   73  1000 0.75  9.999992e-01 1.00000000
224   74  1000 0.75  9.999994e-01 1.00000000
225   75  1000 0.75  9.999996e-01 1.00000000
226   76  1000 0.75  9.999997e-01 1.00000000
227   77  1000 0.75  9.999998e-01 1.00000000
228   78  1000 0.75  9.999998e-01 1.00000000
229   79  1000 0.75  9.999999e-01 1.00000000
230   80  1000 0.75  9.999999e-01 1.00000000
231   81  1000 0.75  9.999999e-01 1.00000000
232   82  1000 0.75  9.999999e-01 1.00000000
233   83  1000 0.75  1.000000e+00 1.00000000
234   84  1000 0.75  1.000000e+00 1.00000000
235   85  1000 0.75  1.000000e+00 1.00000000
236   86  1000 0.75  1.000000e+00 1.00000000
237   87  1000 0.75  1.000000e+00 1.00000000
238   88  1000 0.75  1.000000e+00 1.00000000
239   89  1000 0.75  1.000000e+00 1.00000000
240   90  1000 0.75  1.000000e+00 1.00000000
241   91  1000 0.75  1.000000e+00 1.00000000
242   92  1000 0.75  1.000000e+00 1.00000000
243   93  1000 0.75  1.000000e+00 1.00000000
244   94  1000 0.75  1.000000e+00 1.00000000
245   95  1000 0.75  1.000000e+00 1.00000000
246   96  1000 0.75  1.000000e+00 1.00000000
247   97  1000 0.75  1.000000e+00 1.00000000
248   98  1000 0.75  1.000000e+00 1.00000000
249   99  1000 0.75  1.000000e+00 1.00000000
250  100  1000 0.75  1.000000e+00 1.00000000
251  101  1000 0.75  1.000000e+00 1.00000000
252  102  1000 0.75  1.000000e+00 1.00000000
253  103  1000 0.75  1.000000e+00 1.00000000
254  104  1000 0.75  1.000000e+00 1.00000000
255  105  1000 0.75  1.000000e+00 1.00000000
256  106  1000 0.75  1.000000e+00 1.00000000
257  107  1000 0.75  1.000000e+00 1.00000000
258  108  1000 0.75  1.000000e+00 1.00000000
259  109  1000 0.75  1.000000e+00 1.00000000
260  110  1000 0.75  1.000000e+00 1.00000000
261  111  1000 0.75  1.000000e+00 1.00000000
262  112  1000 0.75  1.000000e+00 1.00000000
263  113  1000 0.75  1.000000e+00 1.00000000
264  114  1000 0.75  1.000000e+00 1.00000000
265  115  1000 0.75  1.000000e+00 1.00000000
266  116  1000 0.75  1.000000e+00 1.00000000
267  117  1000 0.75  1.000000e+00 1.00000000
268  118  1000 0.75  1.000000e+00 1.00000000
269  119  1000 0.75  1.000000e+00 1.00000000
270  120  1000 0.75  1.000000e+00 1.00000000
271  121  1000 0.75  1.000000e+00 1.00000000
272  122  1000 0.75  1.000000e+00 1.00000000
273  123  1000 0.75  1.000000e+00 1.00000000
274  124  1000 0.75  1.000000e+00 1.00000000
275  125  1000 0.75  1.000000e+00 1.00000000
276  126  1000 0.75  1.000000e+00 1.00000000
277  127  1000 0.75  1.000000e+00 1.00000000
278  128  1000 0.75  1.000000e+00 1.00000000
279  129  1000 0.75  1.000000e+00 1.00000000
280  130  1000 0.75  1.000000e+00 1.00000000
281  131  1000 0.75  1.000000e+00 1.00000000
282  132  1000 0.75  1.000000e+00 1.00000000
283  133  1000 0.75  1.000000e+00 1.00000000
284  134  1000 0.75  1.000000e+00 1.00000000
285  135  1000 0.75  1.000000e+00 1.00000000
286  136  1000 0.75  1.000000e+00 1.00000000
287  137  1000 0.75  1.000000e+00 1.00000000
288  138  1000 0.75  1.000000e+00 1.00000000
289  139  1000 0.75  1.000000e+00 1.00000000
290  140  1000 0.75  1.000000e+00 1.00000000
291  141  1000 0.75  1.000000e+00 1.00000000
292  142  1000 0.75  1.000000e+00 1.00000000
293  143  1000 0.75  1.000000e+00 1.00000000
294  144  1000 0.75  1.000000e+00 1.00000000
295  145  1000 0.75  1.000000e+00 1.00000000
296  146  1000 0.75  1.000000e+00 1.00000000
297  147  1000 0.75  1.000000e+00 1.00000000
298  148  1000 0.75  1.000000e+00 1.00000000
299  149  1000 0.75  1.000000e+00 1.00000000
300  150  1000 0.75  1.000000e+00 1.00000000
301    1 10000 0.75  0.000000e+00 0.25000000
302    2 10000 0.75  0.000000e+00 0.43750000
303    3 10000 0.75  0.000000e+00 0.57812500
304    4 10000 0.75  0.000000e+00 0.68359375
305    5 10000 0.75  0.000000e+00 0.76269531
306    6 10000 0.75  0.000000e+00 0.82202148
307    7 10000 0.75  0.000000e+00 0.86651611
308    8 10000 0.75  0.000000e+00 0.89988708
309    9 10000 0.75  0.000000e+00 0.92491531
310   10 10000 0.75 1.893890e-252 0.94368649
311   11 10000 0.75 3.881567e-188 0.95776486
312   12 10000 0.75 1.604654e-140 0.96832365
313   13 10000 0.75 3.785768e-105 0.97624274
314   14 10000 0.75  8.316439e-79 0.98218205
315   15 10000 0.75  3.732075e-59 0.98663654
316   16 10000 0.75  1.789870e-44 0.98997740
317   17 10000 0.75  1.702152e-33 0.99248305
318   18 10000 0.75  2.795490e-25 0.99436229
319   19 10000 0.75  3.961593e-19 0.99577172
320   20 10000 0.75  1.605897e-14 0.99682879
321   21 10000 0.75  4.554052e-11 0.99762159
322   22 10000 0.75  1.762415e-08 0.99821619
323   23 10000 0.75  1.534191e-06 0.99866214
324   24 10000 0.75  4.366559e-05 0.99899661
325   25 10000 0.75  5.376689e-04 0.99924746
326   26 10000 0.75  3.532783e-03 0.99943559
327   27 10000 0.75  1.449498e-02 0.99957669
328   28 10000 0.75  4.178170e-02 0.99968252
329   29 10000 0.75  9.242312e-02 0.99976189
330   30 10000 0.75  1.676326e-01 0.99982142
331   31 10000 0.75  2.619883e-01 0.99986606
332   32 10000 0.75  3.662003e-01 0.99989955
333   33 10000 0.75  4.707531e-01 0.99992466
334   34 10000 0.75  5.683256e-01 0.99994350
335   35 10000 0.75  6.545596e-01 0.99995762
336   36 10000 0.75  7.277172e-01 0.99996822
337   37 10000 0.75  7.879023e-01 0.99997616
338   38 10000 0.75  8.362854e-01 0.99998212
339   39 10000 0.75  8.745125e-01 0.99998659
340   40 10000 0.75  9.043251e-01 0.99998994
341   41 10000 0.75  9.273496e-01 0.99999246
342   42 10000 0.75  9.450018e-01 0.99999434
343   43 10000 0.75  9.584611e-01 0.99999576
344   44 10000 0.75  9.686812e-01 0.99999682
345   45 10000 0.75  9.764177e-01 0.99999761
346   46 10000 0.75  9.822607e-01 0.99999821
347   47 10000 0.75  9.866658e-01 0.99999866
348   48 10000 0.75  9.899826e-01 0.99999899
349   49 10000 0.75  9.924775e-01 0.99999924
350   50 10000 0.75  9.943528e-01 0.99999943
351   51 10000 0.75  9.957616e-01 0.99999958
352   52 10000 0.75  9.968195e-01 0.99999968
353   53 10000 0.75  9.976137e-01 0.99999976
354   54 10000 0.75  9.982097e-01 0.99999982
355   55 10000 0.75  9.986570e-01 0.99999987
356   56 10000 0.75  9.989926e-01 0.99999990
357   57 10000 0.75  9.992443e-01 0.99999992
358   58 10000 0.75  9.994332e-01 0.99999994
359   59 10000 0.75  9.995749e-01 0.99999996
360   60 10000 0.75  9.996811e-01 0.99999997
361   61 10000 0.75  9.997608e-01 0.99999998
362   62 10000 0.75  9.998206e-01 0.99999998
363   63 10000 0.75  9.998655e-01 0.99999999
364   64 10000 0.75  9.998991e-01 0.99999999
365   65 10000 0.75  9.999243e-01 0.99999999
366   66 10000 0.75  9.999432e-01 0.99999999
367   67 10000 0.75  9.999574e-01 1.00000000
368   68 10000 0.75  9.999681e-01 1.00000000
369   69 10000 0.75  9.999761e-01 1.00000000
370   70 10000 0.75  9.999820e-01 1.00000000
371   71 10000 0.75  9.999865e-01 1.00000000
372   72 10000 0.75  9.999899e-01 1.00000000
373   73 10000 0.75  9.999924e-01 1.00000000
374   74 10000 0.75  9.999943e-01 1.00000000
375   75 10000 0.75  9.999957e-01 1.00000000
376   76 10000 0.75  9.999968e-01 1.00000000
377   77 10000 0.75  9.999976e-01 1.00000000
378   78 10000 0.75  9.999982e-01 1.00000000
379   79 10000 0.75  9.999987e-01 1.00000000
380   80 10000 0.75  9.999990e-01 1.00000000
381   81 10000 0.75  9.999992e-01 1.00000000
382   82 10000 0.75  9.999994e-01 1.00000000
383   83 10000 0.75  9.999996e-01 1.00000000
384   84 10000 0.75  9.999997e-01 1.00000000
385   85 10000 0.75  9.999998e-01 1.00000000
386   86 10000 0.75  9.999998e-01 1.00000000
387   87 10000 0.75  9.999999e-01 1.00000000
388   88 10000 0.75  9.999999e-01 1.00000000
389   89 10000 0.75  9.999999e-01 1.00000000
390   90 10000 0.75  9.999999e-01 1.00000000
391   91 10000 0.75  1.000000e+00 1.00000000
392   92 10000 0.75  1.000000e+00 1.00000000
393   93 10000 0.75  1.000000e+00 1.00000000
394   94 10000 0.75  1.000000e+00 1.00000000
395   95 10000 0.75  1.000000e+00 1.00000000
396   96 10000 0.75  1.000000e+00 1.00000000
397   97 10000 0.75  1.000000e+00 1.00000000
398   98 10000 0.75  1.000000e+00 1.00000000
399   99 10000 0.75  1.000000e+00 1.00000000
400  100 10000 0.75  1.000000e+00 1.00000000
401  101 10000 0.75  1.000000e+00 1.00000000
402  102 10000 0.75  1.000000e+00 1.00000000
403  103 10000 0.75  1.000000e+00 1.00000000
404  104 10000 0.75  1.000000e+00 1.00000000
405  105 10000 0.75  1.000000e+00 1.00000000
406  106 10000 0.75  1.000000e+00 1.00000000
407  107 10000 0.75  1.000000e+00 1.00000000
408  108 10000 0.75  1.000000e+00 1.00000000
409  109 10000 0.75  1.000000e+00 1.00000000
410  110 10000 0.75  1.000000e+00 1.00000000
411  111 10000 0.75  1.000000e+00 1.00000000
412  112 10000 0.75  1.000000e+00 1.00000000
413  113 10000 0.75  1.000000e+00 1.00000000
414  114 10000 0.75  1.000000e+00 1.00000000
415  115 10000 0.75  1.000000e+00 1.00000000
416  116 10000 0.75  1.000000e+00 1.00000000
417  117 10000 0.75  1.000000e+00 1.00000000
418  118 10000 0.75  1.000000e+00 1.00000000
419  119 10000 0.75  1.000000e+00 1.00000000
420  120 10000 0.75  1.000000e+00 1.00000000
421  121 10000 0.75  1.000000e+00 1.00000000
422  122 10000 0.75  1.000000e+00 1.00000000
423  123 10000 0.75  1.000000e+00 1.00000000
424  124 10000 0.75  1.000000e+00 1.00000000
425  125 10000 0.75  1.000000e+00 1.00000000
426  126 10000 0.75  1.000000e+00 1.00000000
427  127 10000 0.75  1.000000e+00 1.00000000
428  128 10000 0.75  1.000000e+00 1.00000000
429  129 10000 0.75  1.000000e+00 1.00000000
430  130 10000 0.75  1.000000e+00 1.00000000
431  131 10000 0.75  1.000000e+00 1.00000000
432  132 10000 0.75  1.000000e+00 1.00000000
433  133 10000 0.75  1.000000e+00 1.00000000
434  134 10000 0.75  1.000000e+00 1.00000000
435  135 10000 0.75  1.000000e+00 1.00000000
436  136 10000 0.75  1.000000e+00 1.00000000
437  137 10000 0.75  1.000000e+00 1.00000000
438  138 10000 0.75  1.000000e+00 1.00000000
439  139 10000 0.75  1.000000e+00 1.00000000
440  140 10000 0.75  1.000000e+00 1.00000000
441  141 10000 0.75  1.000000e+00 1.00000000
442  142 10000 0.75  1.000000e+00 1.00000000
443  143 10000 0.75  1.000000e+00 1.00000000
444  144 10000 0.75  1.000000e+00 1.00000000
445  145 10000 0.75  1.000000e+00 1.00000000
446  146 10000 0.75  1.000000e+00 1.00000000
447  147 10000 0.75  1.000000e+00 1.00000000
448  148 10000 0.75  1.000000e+00 1.00000000
449  149 10000 0.75  1.000000e+00 1.00000000
450  150 10000 0.75  1.000000e+00 1.00000000
451    1   100 0.90 1.000000e-100 0.10000000
452    2   100 0.90  7.505162e-73 0.19000000
453    3   100 0.90  1.981204e-57 0.27100000
454    4   100 0.90  4.397619e-47 0.34390000
455    5   100 0.90  1.684423e-39 0.40951000
456    6   100 0.90  1.192418e-33 0.46855900
457    7   100 0.90  5.525120e-29 0.52170310
458    8   100 0.90  3.563472e-25 0.56953279
459    9   100 0.90  5.202914e-22 0.61257951
460   10   100 0.90  2.396323e-19 0.65132156
461   11   100 0.90  4.409616e-17 0.68618940
462   12   100 0.90  3.858828e-15 0.71757046
463   13   100 0.90  1.832395e-13 0.74581342
464   14   100 0.90  5.230080e-12 0.77123208
465   15   100 0.90  9.727575e-11 0.79410887
466   16   100 0.90  1.257952e-09 0.81469798
467   17   100 0.90  1.192326e-08 0.83322818
468   18   100 0.90  8.650816e-08 0.84990536
469   19   100 0.90  4.981203e-07 0.86491483
470   20   100 0.90  2.346318e-06 0.87842335
471   21   100 0.90  9.275623e-06 0.89058101
472   22   100 0.90  3.145406e-05 0.90152291
473   23   100 0.90  9.321855e-05 0.91137062
474   24   100 0.90  2.453616e-04 0.92023356
475   25   100 0.90  5.816125e-04 0.92821020
476   26   100 0.90  1.256708e-03 0.93538918
477   27   100 0.90  2.501418e-03 0.94185026
478   28   100 0.90  4.629083e-03 0.94766524
479   29   100 0.90  8.029233e-03 0.95289871
480   30   100 0.90  1.314664e-02 0.95760884
481   31   100 0.90  2.044762e-02 0.96184796
482   32   100 0.90  3.037851e-02 0.96566316
483   33   100 0.90  4.332295e-02 0.96909685
484   34   100 0.90  5.956459e-02 0.97218716
485   35   100 0.90  7.926035e-02 0.97496844
486   36   100 0.90  1.024271e-01 0.97747160
487   37   100 0.90  1.289419e-01 0.97972444
488   38   100 0.90  1.585548e-01 0.98175200
489   39   100 0.90  1.909095e-01 0.98357680
490   40   100 0.90  2.255709e-01 0.98521912
491   41   100 0.90  2.620534e-01 0.98669721
492   42   100 0.90  2.998490e-01 0.98802748
493   43   100 0.90  3.384518e-01 0.98922474
494   44   100 0.90  3.773785e-01 0.99030226
495   45   100 0.90  4.161841e-01 0.99127204
496   46   100 0.90  4.544724e-01 0.99214483
497   47   100 0.90  4.919019e-01 0.99293035
498   48   100 0.90  5.281889e-01 0.99363731
499   49   100 0.90  5.631059e-01 0.99427358
500   50   100 0.90  5.964796e-01 0.99484622
501   51   100 0.90  6.281861e-01 0.99536160
502   52   100 0.90  6.581453e-01 0.99582544
503   53   100 0.90  6.863155e-01 0.99624290
504   54   100 0.90  7.126875e-01 0.99661861
505   55   100 0.90  7.372787e-01 0.99695675
506   56   100 0.90  7.601279e-01 0.99726107
507   57   100 0.90  7.812909e-01 0.99753497
508   58   100 0.90  8.008356e-01 0.99778147
509   59   100 0.90  8.188393e-01 0.99800332
510   60   100 0.90  8.353849e-01 0.99820299
511   61   100 0.90  8.505587e-01 0.99838269
512   62   100 0.90  8.644482e-01 0.99854442
513   63   100 0.90  8.771406e-01 0.99868998
514   64   100 0.90  8.887215e-01 0.99882098
515   65   100 0.90  8.992736e-01 0.99893888
516   66   100 0.90  9.088764e-01 0.99904500
517   67   100 0.90  9.176058e-01 0.99914050
518   68   100 0.90  9.255331e-01 0.99922645
519   69   100 0.90  9.327257e-01 0.99930380
520   70   100 0.90  9.392463e-01 0.99937342
521   71   100 0.90  9.451534e-01 0.99943608
522   72   100 0.90  9.505013e-01 0.99949247
523   73   100 0.90  9.553400e-01 0.99954322
524   74   100 0.90  9.597156e-01 0.99958890
525   75   100 0.90  9.636706e-01 0.99963001
526   76   100 0.90  9.672440e-01 0.99966701
527   77   100 0.90  9.704712e-01 0.99970031
528   78   100 0.90  9.733848e-01 0.99973028
529   79   100 0.90  9.760144e-01 0.99975725
530   80   100 0.90  9.783871e-01 0.99978153
531   81   100 0.90  9.805274e-01 0.99980337
532   82   100 0.90  9.824577e-01 0.99982304
533   83   100 0.90  9.841981e-01 0.99984073
534   84   100 0.90  9.857671e-01 0.99985666
535   85   100 0.90  9.871813e-01 0.99987099
536   86   100 0.90  9.884558e-01 0.99988389
537   87   100 0.90  9.896043e-01 0.99989550
538   88   100 0.90  9.906390e-01 0.99990595
539   89   100 0.90  9.915712e-01 0.99991536
540   90   100 0.90  9.924109e-01 0.99992382
541   91   100 0.90  9.931673e-01 0.99993144
542   92   100 0.90  9.938484e-01 0.99993830
543   93   100 0.90  9.944619e-01 0.99994447
544   94   100 0.90  9.950143e-01 0.99995002
545   95   100 0.90  9.955118e-01 0.99995502
546   96   100 0.90  9.959597e-01 0.99995952
547   97   100 0.90  9.963630e-01 0.99996356
548   98   100 0.90  9.967261e-01 0.99996721
549   99   100 0.90  9.970530e-01 0.99997049
550  100   100 0.90  9.973473e-01 0.99997344
551  101   100 0.90  9.976123e-01 0.99997609
552  102   100 0.90  9.978508e-01 0.99997849
553  103   100 0.90  9.980655e-01 0.99998064
554  104   100 0.90  9.982588e-01 0.99998257
555  105   100 0.90  9.984328e-01 0.99998432
556  106   100 0.90  9.985894e-01 0.99998588
557  107   100 0.90  9.987304e-01 0.99998730
558  108   100 0.90  9.988573e-01 0.99998857
559  109   100 0.90  9.989715e-01 0.99998971
560  110   100 0.90  9.990743e-01 0.99999074
561  111   100 0.90  9.991668e-01 0.99999166
562  112   100 0.90  9.992501e-01 0.99999250
563  113   100 0.90  9.993251e-01 0.99999325
564  114   100 0.90  9.993925e-01 0.99999392
565  115   100 0.90  9.994533e-01 0.99999453
566  116   100 0.90  9.995079e-01 0.99999508
567  117   100 0.90  9.995571e-01 0.99999557
568  118   100 0.90  9.996014e-01 0.99999601
569  119   100 0.90  9.996413e-01 0.99999641
570  120   100 0.90  9.996771e-01 0.99999677
571  121   100 0.90  9.997094e-01 0.99999709
572  122   100 0.90  9.997385e-01 0.99999738
573  123   100 0.90  9.997646e-01 0.99999765
574  124   100 0.90  9.997882e-01 0.99999788
575  125   100 0.90  9.998093e-01 0.99999809
576  126   100 0.90  9.998284e-01 0.99999828
577  127   100 0.90  9.998456e-01 0.99999846
578  128   100 0.90  9.998610e-01 0.99999861
579  129   100 0.90  9.998749e-01 0.99999875
580  130   100 0.90  9.998874e-01 0.99999887
581  131   100 0.90  9.998987e-01 0.99999899
582  132   100 0.90  9.999088e-01 0.99999909
583  133   100 0.90  9.999179e-01 0.99999918
584  134   100 0.90  9.999261e-01 0.99999926
585  135   100 0.90  9.999335e-01 0.99999934
586  136   100 0.90  9.999402e-01 0.99999940
587  137   100 0.90  9.999461e-01 0.99999946
588  138   100 0.90  9.999515e-01 0.99999952
589  139   100 0.90  9.999564e-01 0.99999956
590  140   100 0.90  9.999607e-01 0.99999961
591  141   100 0.90  9.999647e-01 0.99999965
592  142   100 0.90  9.999682e-01 0.99999968
593  143   100 0.90  9.999714e-01 0.99999971
594  144   100 0.90  9.999742e-01 0.99999974
595  145   100 0.90  9.999768e-01 0.99999977
596  146   100 0.90  9.999791e-01 0.99999979
597  147   100 0.90  9.999812e-01 0.99999981
598  148   100 0.90  9.999831e-01 0.99999983
599  149   100 0.90  9.999848e-01 0.99999985
600  150   100 0.90  9.999863e-01 0.99999986
601    1  1000 0.90  0.000000e+00 0.10000000
602    2  1000 0.90  0.000000e+00 0.19000000
603    3  1000 0.90  0.000000e+00 0.27100000
604    4  1000 0.90  0.000000e+00 0.34390000
605    5  1000 0.90  0.000000e+00 0.40951000
606    6  1000 0.90  0.000000e+00 0.46855900
607    7  1000 0.90 2.651046e-283 0.52170310
608    8  1000 0.90 3.301665e-245 0.56953279
609    9  1000 0.90 1.453673e-213 0.61257951
610   10  1000 0.90 6.243877e-187 0.65132156
611   11  1000 0.90 2.779761e-164 0.68618940
612   12  1000 0.90 7.320725e-145 0.71757046
613   13  1000 0.90 4.267682e-128 0.74581342
614   14  1000 0.90 1.531382e-113 0.77123208
615   15  1000 0.90 7.586577e-101 0.79410887
616   16  1000 0.90  9.922934e-90 0.81469798
617   17  1000 0.90  5.806990e-80 0.83322818
618   18  1000 0.90  2.347311e-71 0.84990536
619   19  1000 0.90  9.404653e-64 0.86491483
620   20  1000 0.90  5.056724e-57 0.87842335
621   21  1000 0.90  4.714447e-51 0.89058101
622   22  1000 0.90  9.479111e-46 0.90152291
623   23  1000 0.90  4.954770e-41 0.91137062
624   24  1000 0.90  7.907989e-37 0.92023356
625   25  1000 0.90  4.429320e-33 0.92821020
626   26  1000 0.90  9.825224e-30 0.93538918
627   27  1000 0.90  9.590989e-27 0.94185026
628   28  1000 0.90  4.518036e-24 0.94766524
629   29  1000 0.90  1.113629e-21 0.95289871
630   30  1000 0.90  1.542223e-19 0.95760884
631   31  1000 0.90  1.277695e-17 0.96184796
632   32  1000 0.90  6.693669e-16 0.96566316
633   33  1000 0.90  2.329056e-14 0.96909685
634   34  1000 0.90  5.621877e-13 0.97218716
635   35  1000 0.90  9.784979e-12 0.97496844
636   36  1000 0.90  1.271008e-10 0.97747160
637   37  1000 0.90  1.270405e-09 0.97972444
638   38  1000 0.90  1.004137e-08 0.98175200
639   39  1000 0.90  6.430946e-08 0.98357680
640   40  1000 0.90  3.410596e-07 0.98521912
641   41  1000 0.90  1.527208e-06 0.98669721
642   42  1000 0.90  5.875244e-06 0.98802748
643   43  1000 0.90  1.972276e-05 0.98922474
644   44  1000 0.90  5.858297e-05 0.99030226
645   45  1000 0.90  1.559032e-04 0.99127204
646   46  1000 0.90  3.759022e-04 0.99214483
647   47  1000 0.90  8.294408e-04 0.99293035
648   48  1000 0.90  1.690022e-03 0.99363731
649   49  1000 0.90  3.205537e-03 0.99427358
650   50  1000 0.90  5.701068e-03 0.99484622
651   51  1000 0.90  9.569365e-03 0.99536160
652   52  1000 0.90  1.524817e-02 0.99582544
653   53  1000 0.90  2.318667e-02 0.99624290
654   54  1000 0.90  3.380584e-02 0.99661861
655   55  1000 0.90  4.745882e-02 0.99695675
656   56  1000 0.90  6.439720e-02 0.99726107
657   57  1000 0.90  8.474760e-02 0.99753497
658   58  1000 0.90  1.085010e-01 0.99778147
659   59  1000 0.90  1.355148e-01 0.99800332
660   60  1000 0.90  1.655260e-01 0.99820299
661   61  1000 0.90  1.981723e-01 0.99838269
662   62  1000 0.90  2.330182e-01 0.99854442
663   63  1000 0.90  2.695829e-01 0.99868998
664   64  1000 0.90  3.073666e-01 0.99882098
665   65  1000 0.90  3.458743e-01 0.99893888
666   66  1000 0.90  3.846347e-01 0.99904500
667   67  1000 0.90  4.232154e-01 0.99914050
668   68  1000 0.90  4.612323e-01 0.99922645
669   69  1000 0.90  4.983558e-01 0.99930380
670   70  1000 0.90  5.343121e-01 0.99937342
671   71  1000 0.90  5.688833e-01 0.99943608
672   72  1000 0.90  6.019038e-01 0.99949247
673   73  1000 0.90  6.332562e-01 0.99954322
674   74  1000 0.90  6.628657e-01 0.99958890
675   75  1000 0.90  6.906950e-01 0.99963001
676   76  1000 0.90  7.167379e-01 0.99966701
677   77  1000 0.90  7.410141e-01 0.99970031
678   78  1000 0.90  7.635643e-01 0.99973028
679   79  1000 0.90  7.844449e-01 0.99975725
680   80  1000 0.90  8.037248e-01 0.99978153
681   81  1000 0.90  8.214811e-01 0.99980337
682   82  1000 0.90  8.377965e-01 0.99982304
683   83  1000 0.90  8.527570e-01 0.99984073
684   84  1000 0.90  8.664496e-01 0.99985666
685   85  1000 0.90  8.789605e-01 0.99987099
686   86  1000 0.90  8.903746e-01 0.99988389
687   87  1000 0.90  9.007738e-01 0.99989550
688   88  1000 0.90  9.102368e-01 0.99990595
689   89  1000 0.90  9.188383e-01 0.99991536
690   90  1000 0.90  9.266492e-01 0.99992382
691   91  1000 0.90  9.337356e-01 0.99993144
692   92  1000 0.90  9.401597e-01 0.99993830
693   93  1000 0.90  9.459791e-01 0.99994447
694   94  1000 0.90  9.512473e-01 0.99995002
695   95  1000 0.90  9.560138e-01 0.99995502
696   96  1000 0.90  9.603240e-01 0.99995952
697   97  1000 0.90  9.642198e-01 0.99996356
698   98  1000 0.90  9.677395e-01 0.99996721
699   99  1000 0.90  9.709182e-01 0.99997049
700  100  1000 0.90  9.737879e-01 0.99997344
701  101  1000 0.90  9.763779e-01 0.99997609
702  102  1000 0.90  9.787148e-01 0.99997849
703  103  1000 0.90  9.808228e-01 0.99998064
704  104  1000 0.90  9.827239e-01 0.99998257
705  105  1000 0.90  9.844380e-01 0.99998432
706  106  1000 0.90  9.859832e-01 0.99998588
707  107  1000 0.90  9.873760e-01 0.99998730
708  108  1000 0.90  9.886312e-01 0.99998857
709  109  1000 0.90  9.897623e-01 0.99998971
710  110  1000 0.90  9.907813e-01 0.99999074
711  111  1000 0.90  9.916994e-01 0.99999166
712  112  1000 0.90  9.925263e-01 0.99999250
713  113  1000 0.90  9.932712e-01 0.99999325
714  114  1000 0.90  9.939420e-01 0.99999392
715  115  1000 0.90  9.945462e-01 0.99999453
716  116  1000 0.90  9.950902e-01 0.99999508
717  117  1000 0.90  9.955801e-01 0.99999557
718  118  1000 0.90  9.960212e-01 0.99999601
719  119  1000 0.90  9.964184e-01 0.99999641
720  120  1000 0.90  9.967760e-01 0.99999677
721  121  1000 0.90  9.970979e-01 0.99999709
722  122  1000 0.90  9.973877e-01 0.99999738
723  123  1000 0.90  9.976486e-01 0.99999765
724  124  1000 0.90  9.978835e-01 0.99999788
725  125  1000 0.90  9.980950e-01 0.99999809
726  126  1000 0.90  9.982853e-01 0.99999828
727  127  1000 0.90  9.984567e-01 0.99999846
728  128  1000 0.90  9.986109e-01 0.99999861
729  129  1000 0.90  9.987497e-01 0.99999875
730  130  1000 0.90  9.988747e-01 0.99999887
731  131  1000 0.90  9.989871e-01 0.99999899
732  132  1000 0.90  9.990884e-01 0.99999909
733  133  1000 0.90  9.991795e-01 0.99999918
734  134  1000 0.90  9.992615e-01 0.99999926
735  135  1000 0.90  9.993353e-01 0.99999934
736  136  1000 0.90  9.994018e-01 0.99999940
737  137  1000 0.90  9.994616e-01 0.99999946
738  138  1000 0.90  9.995154e-01 0.99999952
739  139  1000 0.90  9.995639e-01 0.99999956
740  140  1000 0.90  9.996075e-01 0.99999961
741  141  1000 0.90  9.996467e-01 0.99999965
742  142  1000 0.90  9.996820e-01 0.99999968
743  143  1000 0.90  9.997138e-01 0.99999971
744  144  1000 0.90  9.997424e-01 0.99999974
745  145  1000 0.90  9.997682e-01 0.99999977
746  146  1000 0.90  9.997914e-01 0.99999979
747  147  1000 0.90  9.998122e-01 0.99999981
748  148  1000 0.90  9.998310e-01 0.99999983
749  149  1000 0.90  9.998479e-01 0.99999985
750  150  1000 0.90  9.998631e-01 0.99999986
751    1 10000 0.90  0.000000e+00 0.10000000
752    2 10000 0.90  0.000000e+00 0.19000000
753    3 10000 0.90  0.000000e+00 0.27100000
754    4 10000 0.90  0.000000e+00 0.34390000
755    5 10000 0.90  0.000000e+00 0.40951000
756    6 10000 0.90  0.000000e+00 0.46855900
757    7 10000 0.90  0.000000e+00 0.52170310
758    8 10000 0.90  0.000000e+00 0.56953279
759    9 10000 0.90  0.000000e+00 0.61257951
760   10 10000 0.90  0.000000e+00 0.65132156
761   11 10000 0.90  0.000000e+00 0.68618940
762   12 10000 0.90  0.000000e+00 0.71757046
763   13 10000 0.90  0.000000e+00 0.74581342
764   14 10000 0.90  0.000000e+00 0.77123208
765   15 10000 0.90  0.000000e+00 0.79410887
766   16 10000 0.90  0.000000e+00 0.81469798
767   17 10000 0.90  0.000000e+00 0.83322818
768   18 10000 0.90  0.000000e+00 0.84990536
769   19 10000 0.90  0.000000e+00 0.86491483
770   20 10000 0.90  0.000000e+00 0.87842335
771   21 10000 0.90  0.000000e+00 0.89058101
772   22 10000 0.90  0.000000e+00 0.90152291
773   23 10000 0.90  0.000000e+00 0.91137062
774   24 10000 0.90  0.000000e+00 0.92023356
775   25 10000 0.90 4.940656e-324 0.92821020
776   26 10000 0.90 8.383487e-291 0.93538918
777   27 10000 0.90 6.586184e-261 0.94185026
778   28 10000 0.90 3.544023e-234 0.94766524
779   29 10000 0.90 2.933621e-210 0.95289871
780   30 10000 0.90 7.611550e-189 0.95760884
781   31 10000 0.90 1.159501e-169 0.96184796
782   32 10000 0.90 1.805686e-152 0.96566316
783   33 10000 0.90 4.696773e-137 0.96909685
784   34 10000 0.90 3.153652e-123 0.97218716
785   35 10000 0.90 8.046351e-111 0.97496844
786   36 10000 0.90  1.100227e-99 0.97747160
787   37 10000 0.90  1.095019e-89 0.97972444
788   38 10000 0.90  1.042151e-80 0.98175200
789   39 10000 0.90  1.209898e-72 0.98357680
790   40 10000 0.90  2.129621e-65 0.98521912
791   41 10000 0.90  6.902103e-59 0.98669721
792   42 10000 0.90  4.900710e-53 0.98802748
793   43 10000 0.90  8.905883e-48 0.98922474
794   44 10000 0.90  4.761168e-43 0.99030226
795   45 10000 0.90  8.483010e-39 0.99127204
796   46 10000 0.90  5.633115e-35 0.99214483
797   47 10000 0.90  1.541181e-31 0.99293035
798   48 10000 0.90  1.900746e-28 0.99363731
799   49 10000 0.90  1.145534e-25 0.99427358
800   50 10000 0.90  3.627124e-23 0.99484622
801   51 10000 0.90  6.439189e-21 0.99536160
802   52 10000 0.90  6.794814e-19 0.99582544
803   53 10000 0.90  4.491420e-17 0.99624290
804   54 10000 0.90  1.949473e-15 0.99661861
805   55 10000 0.90  5.796550e-14 0.99695675
806   56 10000 0.90  1.226506e-12 0.99726107
807   57 10000 0.90  1.911058e-11 0.99753497
808   58 10000 0.90  2.261193e-10 0.99778147
809   59 10000 0.90  2.088664e-09 0.99800332
810   60 10000 0.90  1.544055e-08 0.99820299
811   61 10000 0.90  9.341768e-08 0.99838269
812   62 10000 0.90  4.719526e-07 0.99854442
813   63 10000 0.90  2.027325e-06 0.99868998
814   64 10000 0.90  7.526048e-06 0.99882098
815   65 10000 0.90  2.450092e-05 0.99893888
816   66 10000 0.90  7.087360e-05 0.99904500
817   67 10000 0.90  1.843378e-04 0.99914050
818   68 10000 0.90  4.357100e-04 0.99922645
819   69 10000 0.90  9.449196e-04 0.99930380
820   70 10000 0.90  1.896488e-03 0.99937342
821   71 10000 0.90  3.550029e-03 0.99943608
822   72 10000 0.90  6.241241e-03 0.99949247
823   73 10000 0.90  1.037037e-02 0.99954322
824   74 10000 0.90  1.637780e-02 0.99958890
825   75 10000 0.90  2.470945e-02 0.99963001
826   76 10000 0.90  3.577697e-02 0.99966701
827   77 10000 0.90  4.991888e-02 0.99970031
828   78 10000 0.90  6.736836e-02 0.99973028
829   79 10000 0.90  8.823169e-02 0.99975725
830   80 10000 0.90  1.124796e-01 0.99978153
831   81 10000 0.90  1.399509e-01 0.99980337
832   82 10000 0.90  1.703670e-01 0.99982304
833   83 10000 0.90  2.033542e-01 0.99984073
834   84 10000 0.90  2.384695e-01 0.99985666
835   85 10000 0.90  2.752286e-01 0.99987099
836   86 10000 0.90  3.131320e-01 0.99988389
837   87 10000 0.90  3.516878e-01 0.99989550
838   88 10000 0.90  3.904305e-01 0.99990595
839   89 10000 0.90  4.289346e-01 0.99991536
840   90 10000 0.90  4.668242e-01 0.99992382
841   91 10000 0.90  5.037780e-01 0.99993144
842   92 10000 0.90  5.395307e-01 0.99993830
843   93 10000 0.90  5.738724e-01 0.99994447
844   94 10000 0.90  6.066447e-01 0.99995002
845   95 10000 0.90  6.377367e-01 0.99995502
846   96 10000 0.90  6.670796e-01 0.99995952
847   97 10000 0.90  6.946407e-01 0.99996356
848   98 10000 0.90  7.204179e-01 0.99996721
849   99 10000 0.90  7.444341e-01 0.99997049
850  100 10000 0.90  7.667323e-01 0.99997344
851  101 10000 0.90  7.873712e-01 0.99997609
852  102 10000 0.90  8.064208e-01 0.99997849
853  103 10000 0.90  8.239590e-01 0.99998064
854  104 10000 0.90  8.400693e-01 0.99998257
855  105 10000 0.90  8.548377e-01 0.99998432
856  106 10000 0.90  8.683511e-01 0.99998588
857  107 10000 0.90  8.806957e-01 0.99998730
858  108 10000 0.90  8.919557e-01 0.99998857
859  109 10000 0.90  9.022128e-01 0.99998971
860  110 10000 0.90  9.115450e-01 0.99999074
861  111 10000 0.90  9.200265e-01 0.99999166
862  112 10000 0.90  9.277272e-01 0.99999250
863  113 10000 0.90  9.347130e-01 0.99999325
864  114 10000 0.90  9.410452e-01 0.99999392
865  115 10000 0.90  9.467808e-01 0.99999453
866  116 10000 0.90  9.519727e-01 0.99999508
867  117 10000 0.90  9.566698e-01 0.99999557
868  118 10000 0.90  9.609169e-01 0.99999601
869  119 10000 0.90  9.647555e-01 0.99999641
870  120 10000 0.90  9.682233e-01 0.99999677
871  121 10000 0.90  9.713550e-01 0.99999709
872  122 10000 0.90  9.741822e-01 0.99999738
873  123 10000 0.90  9.767337e-01 0.99999765
874  124 10000 0.90  9.790358e-01 0.99999788
875  125 10000 0.90  9.811123e-01 0.99999809
876  126 10000 0.90  9.829849e-01 0.99999828
877  127 10000 0.90  9.846733e-01 0.99999846
878  128 10000 0.90  9.861953e-01 0.99999861
879  129 10000 0.90  9.875672e-01 0.99999875
880  130 10000 0.90  9.888035e-01 0.99999887
881  131 10000 0.90  9.899175e-01 0.99999899
882  132 10000 0.90  9.909211e-01 0.99999909
883  133 10000 0.90  9.918253e-01 0.99999918
884  134 10000 0.90  9.926397e-01 0.99999926
885  135 10000 0.90  9.933733e-01 0.99999934
886  136 10000 0.90  9.940340e-01 0.99999940
887  137 10000 0.90  9.946290e-01 0.99999946
888  138 10000 0.90  9.951648e-01 0.99999952
889  139 10000 0.90  9.956473e-01 0.99999956
890  140 10000 0.90  9.960817e-01 0.99999961
891  141 10000 0.90  9.964728e-01 0.99999965
892  142 10000 0.90  9.968250e-01 0.99999968
893  143 10000 0.90  9.971420e-01 0.99999971
894  144 10000 0.90  9.974275e-01 0.99999974
895  145 10000 0.90  9.976844e-01 0.99999977
896  146 10000 0.90  9.979157e-01 0.99999979
897  147 10000 0.90  9.981240e-01 0.99999981
898  148 10000 0.90  9.983114e-01 0.99999983
899  149 10000 0.90  9.984801e-01 0.99999985
900  150 10000 0.90  9.986320e-01 0.99999986
901    1   100 0.99 1.000000e-200 0.01000000
902    2   100 0.99 7.679053e-171 0.01990000
903    3   100 0.99 1.892811e-153 0.02970100
904    4   100 0.99 3.581129e-141 0.03940399
905    5   100 0.99 1.067643e-131 0.04900995
906    6   100 0.99 5.374287e-124 0.05851985
907    7   100 0.99 1.618585e-117 0.06793465
908    8   100 0.99 6.206281e-112 0.07725531
909    9   100 0.99 4.931174e-107 0.08648275
910   10   100 0.99 1.132222e-102 0.09561792
911   11   100 0.99  9.523519e-99 0.10466175
912   12   100 0.99  3.496361e-95 0.11361513
913   13   100 0.99  6.399632e-92 0.12247898
914   14   100 0.99  6.476147e-89 0.13125419
915   15   100 0.99  3.932761e-86 0.13994165
916   16   100 0.99  1.531065e-83 0.14854223
917   17   100 0.99  4.033446e-81 0.15705681
918   18   100 0.99  7.519491e-79 0.16548624
919   19   100 0.99  1.029952e-76 0.17383138
920   20   100 0.99  1.069892e-74 0.18209306
921   21   100 0.99  8.660010e-73 0.19027213
922   22   100 0.99  5.590752e-71 0.19836941
923   23   100 0.99  2.937404e-69 0.20638572
924   24   100 0.99  1.278341e-67 0.21432186
925   25   100 0.99  4.679835e-66 0.22217864
926   26   100 0.99  1.460952e-64 0.22995685
927   27   100 0.99  3.936527e-63 0.23765729
928   28   100 0.99  9.254223e-62 0.24528071
929   29   100 0.99  1.916464e-60 0.25282791
930   30   100 0.99  3.526586e-59 0.26029963
931   31   100 0.99  5.811530e-58 0.26769663
932   32   100 0.99  8.637235e-57 0.27501966
933   33   100 0.99  1.165173e-55 0.28226947
934   34   100 0.99  1.435064e-54 0.28944677
935   35   100 0.99  1.622297e-53 0.29655231
936   36   100 0.99  1.691554e-52 0.30358678
937   37   100 0.99  1.634110e-51 0.31055091
938   38   100 0.99  1.468603e-50 0.31744540
939   39   100 0.99  1.232550e-49 0.32427095
940   40   100 0.99  9.694037e-49 0.33102824
941   41   100 0.99  7.168290e-48 0.33771796
942   42   100 0.99  4.998570e-47 0.34434078
943   43   100 0.99  3.296185e-46 0.35089737
944   44   100 0.99  2.060843e-45 0.35738840
945   45   100 0.99  1.224622e-44 0.36381451
946   46   100 0.99  6.932168e-44 0.37017637
947   47   100 0.99  3.746007e-43 0.37647461
948   48   100 0.99  1.936266e-42 0.38270986
949   49   100 0.99  9.591115e-42 0.38888276
950   50   100 0.99  4.560815e-41 0.39499393
951   51   100 0.99  2.085459e-40 0.40104399
952   52   100 0.99  9.183773e-40 0.40703355
953   53   100 0.99  3.900651e-39 0.41296322
954   54   100 0.99  1.600111e-38 0.41883359
955   55   100 0.99  6.347856e-38 0.42464525
956   56   100 0.99  2.438400e-37 0.43039880
957   57   100 0.99  9.080124e-37 0.43609481
958   58   100 0.99  3.281476e-36 0.44173386
959   59   100 0.99  1.152110e-35 0.44731652
960   60   100 0.99  3.933690e-35 0.45284336
961   61   100 0.99  1.307374e-34 0.45831492
962   62   100 0.99  4.233363e-34 0.46373177
963   63   100 0.99  1.336688e-33 0.46909446
964   64   100 0.99  4.118979e-33 0.47440351
965   65   100 0.99  1.239661e-32 0.47965948
966   66   100 0.99  3.646649e-32 0.48486288
967   67   100 0.99  1.049231e-31 0.49001425
968   68   100 0.99  2.954816e-31 0.49511411
969   69   100 0.99  8.149923e-31 0.50016297
970   70   100 0.99  2.202981e-30 0.50516134
971   71   100 0.99  5.839296e-30 0.51010973
972   72   100 0.99  1.518625e-29 0.51500863
973   73   100 0.99  3.877203e-29 0.51985854
974   74   100 0.99  9.722815e-29 0.52465996
975   75   100 0.99  2.396015e-28 0.52941336
976   76   100 0.99  5.805251e-28 0.53411922
977   77   100 0.99  1.383528e-27 0.53877803
978   78   100 0.99  3.244773e-27 0.54339025
979   79   100 0.99  7.491976e-27 0.54795635
980   80   100 0.99  1.703741e-26 0.55247679
981   81   100 0.99  3.817493e-26 0.55695202
982   82   100 0.99  8.431151e-26 0.56138250
983   83   100 0.99  1.836072e-25 0.56576867
984   84   100 0.99  3.944037e-25 0.57011099
985   85   100 0.99  8.359684e-25 0.57440988
986   86   100 0.99  1.748960e-24 0.57866578
987   87   100 0.99  3.612849e-24 0.58287912
988   88   100 0.99  7.371121e-24 0.58705033
989   89   100 0.99  1.485801e-23 0.59117983
990   90   100 0.99  2.959754e-23 0.59526803
991   91   100 0.99  5.828273e-23 0.59931535
992   92   100 0.99  1.134828e-22 0.60332219
993   93   100 0.99  2.185443e-22 0.60728897
994   94   100 0.99  4.163679e-22 0.61121608
995   95   100 0.99  7.849637e-22 0.61510392
996   96   100 0.99  1.464735e-21 0.61895288
997   97   100 0.99  2.705857e-21 0.62276335
998   98   100 0.99  4.949753e-21 0.62653572
999   99   100 0.99  8.967854e-21 0.63027036
1000 100   100 0.99  1.609572e-20 0.63396766
1001 101   100 0.99  2.862442e-20 0.63762798
1002 102   100 0.99  5.044906e-20 0.64125170
1003 103   100 0.99  8.813371e-20 0.64483919
1004 104   100 0.99  1.526455e-19 0.64839079
1005 105   100 0.99  2.621542e-19 0.65190689
1006 106   100 0.99  4.465153e-19 0.65538782
1007 107   100 0.99  7.543906e-19 0.65883394
1008 108   100 0.99  1.264469e-18 0.66224560
1009 109   100 0.99  2.103010e-18 0.66562314
1010 110   100 0.99  3.471073e-18 0.66896691
1011 111   100 0.99  5.686447e-18 0.67227724
1012 112   100 0.99  9.247774e-18 0.67555447
1013 113   100 0.99  1.493188e-17 0.67879893
1014 114   100 0.99  2.394054e-17 0.68201094
1015 115   100 0.99  3.812010e-17 0.68519083
1016 116   100 0.99  6.028823e-17 0.68833892
1017 117   100 0.99  9.471645e-17 0.69145553
1018 118   100 0.99  1.478384e-16 0.69454097
1019 119   100 0.99  2.292826e-16 0.69759556
1020 120   100 0.99  3.533693e-16 0.70061961
1021 121   100 0.99  5.412663e-16 0.70361341
1022 122   100 0.99  8.240750e-16 0.70657728
1023 123   100 0.99  1.247223e-15 0.70951151
1024 124   100 0.99  1.876680e-15 0.71241639
1025 125   100 0.99  2.807699e-15 0.71529223
1026 126   100 0.99  4.177050e-15 0.71813930
1027 127   100 0.99  6.180039e-15 0.72095791
1028 128   100 0.99  9.094056e-15 0.72374833
1029 129   100 0.99  1.331099e-14 0.72651085
1030 130   100 0.99  1.938162e-14 0.72924574
1031 131   100 0.99  2.807607e-14 0.73195328
1032 132   100 0.99  4.046576e-14 0.73463375
1033 133   100 0.99  5.803393e-14 0.73728741
1034 134   100 0.99  8.282398e-14 0.73991454
1035 135   100 0.99  1.176376e-13 0.74251539
1036 136   100 0.99  1.662981e-13 0.74509024
1037 137   100 0.99  2.339992e-13 0.74763934
1038 138   100 0.99  3.277636e-13 0.75016294
1039 139   100 0.99  4.570455e-13 0.75266131
1040 140   100 0.99  6.345163e-13 0.75513470
1041 141   100 0.99  8.770864e-13 0.75758335
1042 142   100 0.99  1.207227e-12 0.76000752
1043 143   100 0.99  1.654676e-12 0.76240745
1044 144   100 0.99  2.258622e-12 0.76478337
1045 145   100 0.99  3.070507e-12 0.76713554
1046 146   100 0.99  4.157582e-12 0.76946418
1047 147   100 0.99  5.607424e-12 0.77176954
1048 148   100 0.99  7.533642e-12 0.77405184
1049 149   100 0.99  1.008306e-11 0.77631133
1050 150   100 0.99  1.344470e-11 0.77854821
1051   1  1000 0.99  0.000000e+00 0.01000000
1052   2  1000 0.99  0.000000e+00 0.01990000
1053   3  1000 0.99  0.000000e+00 0.02970100
1054   4  1000 0.99  0.000000e+00 0.03940399
1055   5  1000 0.99  0.000000e+00 0.04900995
1056   6  1000 0.99  0.000000e+00 0.05851985
1057   7  1000 0.99  0.000000e+00 0.06793465
1058   8  1000 0.99  0.000000e+00 0.07725531
1059   9  1000 0.99  0.000000e+00 0.08648275
1060  10  1000 0.99  0.000000e+00 0.09561792
1061  11  1000 0.99  0.000000e+00 0.10466175
1062  12  1000 0.99  0.000000e+00 0.11361513
1063  13  1000 0.99  0.000000e+00 0.12247898
1064  14  1000 0.99  0.000000e+00 0.13125419
1065  15  1000 0.99  0.000000e+00 0.13994165
1066  16  1000 0.99  0.000000e+00 0.14854223
1067  17  1000 0.99  0.000000e+00 0.15705681
1068  18  1000 0.99  0.000000e+00 0.16548624
1069  19  1000 0.99  0.000000e+00 0.17383138
1070  20  1000 0.99  0.000000e+00 0.18209306
1071  21  1000 0.99  0.000000e+00 0.19027213
1072  22  1000 0.99  0.000000e+00 0.19836941
1073  23  1000 0.99  0.000000e+00 0.20638572
1074  24  1000 0.99  0.000000e+00 0.21432186
1075  25  1000 0.99  0.000000e+00 0.22217864
1076  26  1000 0.99  0.000000e+00 0.22995685
1077  27  1000 0.99  0.000000e+00 0.23765729
1078  28  1000 0.99  0.000000e+00 0.24528071
1079  29  1000 0.99  0.000000e+00 0.25282791
1080  30  1000 0.99  0.000000e+00 0.26029963
1081  31  1000 0.99  0.000000e+00 0.26769663
1082  32  1000 0.99  0.000000e+00 0.27501966
1083  33  1000 0.99  0.000000e+00 0.28226947
1084  34  1000 0.99  0.000000e+00 0.28944677
1085  35  1000 0.99  0.000000e+00 0.29655231
1086  36  1000 0.99  0.000000e+00 0.30358678
1087  37  1000 0.99  0.000000e+00 0.31055091
1088  38  1000 0.99  0.000000e+00 0.31744540
1089  39  1000 0.99  0.000000e+00 0.32427095
1090  40  1000 0.99  0.000000e+00 0.33102824
1091  41  1000 0.99  0.000000e+00 0.33771796
1092  42  1000 0.99  0.000000e+00 0.34434078
1093  43  1000 0.99  0.000000e+00 0.35089737
1094  44  1000 0.99  0.000000e+00 0.35738840
1095  45  1000 0.99  0.000000e+00 0.36381451
1096  46  1000 0.99  0.000000e+00 0.37017637
1097  47  1000 0.99  0.000000e+00 0.37647461
1098  48  1000 0.99  0.000000e+00 0.38270986
1099  49  1000 0.99  0.000000e+00 0.38888276
1100  50  1000 0.99  0.000000e+00 0.39499393
1101  51  1000 0.99  0.000000e+00 0.40104399
1102  52  1000 0.99  0.000000e+00 0.40703355
1103  53  1000 0.99  0.000000e+00 0.41296322
1104  54  1000 0.99  0.000000e+00 0.41883359
1105  55  1000 0.99  0.000000e+00 0.42464525
1106  56  1000 0.99  0.000000e+00 0.43039880
1107  57  1000 0.99  0.000000e+00 0.43609481
1108  58  1000 0.99  0.000000e+00 0.44173386
1109  59  1000 0.99  0.000000e+00 0.44731652
1110  60  1000 0.99  0.000000e+00 0.45284336
1111  61  1000 0.99  0.000000e+00 0.45831492
1112  62  1000 0.99  0.000000e+00 0.46373177
1113  63  1000 0.99  0.000000e+00 0.46909446
1114  64  1000 0.99  0.000000e+00 0.47440351
1115  65  1000 0.99 8.571051e-320 0.47965948
1116  66  1000 0.99 4.158523e-315 0.48486288
1117  67  1000 0.99 1.617012e-310 0.49001425
1118  68  1000 0.99 5.073461e-306 0.49511411
1119  69  1000 0.99 1.292812e-301 0.50016297
1120  70  1000 0.99 2.692198e-297 0.50516134
1121  71  1000 0.99 4.608981e-293 0.51010973
1122  72  1000 0.99 6.523886e-289 0.51500863
1123  73  1000 0.99 7.676895e-285 0.51985854
1124  74  1000 0.99 7.549534e-281 0.52465996
1125  75  1000 0.99 6.235847e-277 0.52941336
1126  76  1000 0.99 4.347204e-273 0.53411922
1127  77  1000 0.99 2.569686e-269 0.53877803
1128  78  1000 0.99 1.293729e-265 0.54339025
1129  79  1000 0.99 5.571395e-262 0.54795635
1130  80  1000 0.99 2.060795e-258 0.55247679
1131  81  1000 0.99 6.573280e-255 0.55695202
1132  82  1000 0.99 1.814967e-251 0.56138250
1133  83  1000 0.99 4.354084e-248 0.56576867
1134  84  1000 0.99 9.107733e-245 0.57011099
1135  85  1000 0.99 1.666858e-241 0.57440988
1136  86  1000 0.99 2.677929e-238 0.57866578
1137  87  1000 0.99 3.788770e-235 0.58287912
1138  88  1000 0.99 4.735171e-232 0.58705033
1139  89  1000 0.99 5.243304e-229 0.59117983
1140  90  1000 0.99 5.158894e-226 0.59526803
1141  91  1000 0.99 4.522714e-223 0.59931535
1142  92  1000 0.99 3.542431e-220 0.60332219
1143  93  1000 0.99 2.485389e-217 0.60728897
1144  94  1000 0.99 1.565931e-214 0.61121608
1145  95  1000 0.99 8.881688e-212 0.61510392
1146  96  1000 0.99 4.545581e-209 0.61895288
1147  97  1000 0.99 2.104012e-206 0.62276335
1148  98  1000 0.99 8.827458e-204 0.62653572
1149  99  1000 0.99 3.364228e-201 0.63027036
1150 100  1000 0.99 1.167087e-198 0.63396766
1151 101  1000 0.99 3.692901e-196 0.63762798
1152 102  1000 0.99 1.067901e-193 0.64125170
1153 103  1000 0.99 2.827617e-191 0.64483919
1154 104  1000 0.99 6.868148e-189 0.64839079
1155 105  1000 0.99 1.533092e-186 0.65190689
1156 106  1000 0.99 3.150386e-184 0.65538782
1157 107  1000 0.99 5.969842e-182 0.65883394
1158 108  1000 0.99 1.044915e-179 0.66224560
1159 109  1000 0.99 1.692051e-177 0.66562314
1160 110  1000 0.99 2.538852e-175 0.66896691
1161 111  1000 0.99 3.535168e-173 0.67227724
1162 112  1000 0.99 4.574799e-171 0.67555447
1163 113  1000 0.99 5.509931e-169 0.67879893
1164 114  1000 0.99 6.184986e-167 0.68201094
1165 115  1000 0.99 6.479479e-165 0.68519083
1166 116  1000 0.99 6.343445e-163 0.68833892
1167 117  1000 0.99 5.811040e-161 0.69145553
1168 118  1000 0.99 4.987372e-159 0.69454097
1169 119  1000 0.99 4.015230e-157 0.69759556
1170 120  1000 0.99 3.035904e-155 0.70061961
1171 121  1000 0.99 2.158289e-153 0.70361341
1172 122  1000 0.99 1.444334e-151 0.70657728
1173 123  1000 0.99 9.108409e-150 0.70951151
1174 124  1000 0.99 5.418796e-148 0.71241639
1175 125  1000 0.99 3.044426e-146 0.71529223
1176 126  1000 0.99 1.616951e-144 0.71813930
1177 127  1000 0.99 8.126657e-143 0.72095791
1178 128  1000 0.99 3.868798e-141 0.72374833
1179 129  1000 0.99 1.746240e-139 0.72651085
1180 130  1000 0.99 7.479991e-138 0.72924574
1181 131  1000 0.99 3.043428e-136 0.73195328
1182 132  1000 0.99 1.177272e-134 0.73463375
1183 133  1000 0.99 4.333308e-133 0.73728741
1184 134  1000 0.99 1.519011e-131 0.73991454
1185 135  1000 0.99 5.075298e-130 0.74251539
1186 136  1000 0.99 1.617611e-128 0.74509024
1187 137  1000 0.99 4.922023e-127 0.74763934
1188 138  1000 0.99 1.430893e-125 0.75016294
1189 139  1000 0.99 3.977355e-124 0.75266131
1190 140  1000 0.99 1.057860e-122 0.75513470
1191 141  1000 0.99 2.694161e-121 0.75758335
1192 142  1000 0.99 6.574909e-120 0.76000752
1193 143  1000 0.99 1.538611e-118 0.76240745
1194 144  1000 0.99 3.454906e-117 0.76478337
1195 145  1000 0.99 7.449063e-116 0.76713554
1196 146  1000 0.99 1.543151e-114 0.76946418
1197 147  1000 0.99 3.073505e-113 0.77176954
1198 148  1000 0.99 5.889112e-112 0.77405184
1199 149  1000 0.99 1.086231e-110 0.77631133
1200 150  1000 0.99 1.929799e-109 0.77854821
1201   1 10000 0.99  0.000000e+00 0.01000000
1202   2 10000 0.99  0.000000e+00 0.01990000
1203   3 10000 0.99  0.000000e+00 0.02970100
1204   4 10000 0.99  0.000000e+00 0.03940399
1205   5 10000 0.99  0.000000e+00 0.04900995
1206   6 10000 0.99  0.000000e+00 0.05851985
1207   7 10000 0.99  0.000000e+00 0.06793465
1208   8 10000 0.99  0.000000e+00 0.07725531
1209   9 10000 0.99  0.000000e+00 0.08648275
1210  10 10000 0.99  0.000000e+00 0.09561792
1211  11 10000 0.99  0.000000e+00 0.10466175
1212  12 10000 0.99  0.000000e+00 0.11361513
1213  13 10000 0.99  0.000000e+00 0.12247898
1214  14 10000 0.99  0.000000e+00 0.13125419
1215  15 10000 0.99  0.000000e+00 0.13994165
1216  16 10000 0.99  0.000000e+00 0.14854223
1217  17 10000 0.99  0.000000e+00 0.15705681
1218  18 10000 0.99  0.000000e+00 0.16548624
1219  19 10000 0.99  0.000000e+00 0.17383138
1220  20 10000 0.99  0.000000e+00 0.18209306
1221  21 10000 0.99  0.000000e+00 0.19027213
1222  22 10000 0.99  0.000000e+00 0.19836941
1223  23 10000 0.99  0.000000e+00 0.20638572
1224  24 10000 0.99  0.000000e+00 0.21432186
1225  25 10000 0.99  0.000000e+00 0.22217864
1226  26 10000 0.99  0.000000e+00 0.22995685
1227  27 10000 0.99  0.000000e+00 0.23765729
1228  28 10000 0.99  0.000000e+00 0.24528071
1229  29 10000 0.99  0.000000e+00 0.25282791
1230  30 10000 0.99  0.000000e+00 0.26029963
1231  31 10000 0.99  0.000000e+00 0.26769663
1232  32 10000 0.99  0.000000e+00 0.27501966
1233  33 10000 0.99  0.000000e+00 0.28226947
1234  34 10000 0.99  0.000000e+00 0.28944677
1235  35 10000 0.99  0.000000e+00 0.29655231
1236  36 10000 0.99  0.000000e+00 0.30358678
1237  37 10000 0.99  0.000000e+00 0.31055091
1238  38 10000 0.99  0.000000e+00 0.31744540
1239  39 10000 0.99  0.000000e+00 0.32427095
1240  40 10000 0.99  0.000000e+00 0.33102824
1241  41 10000 0.99  0.000000e+00 0.33771796
1242  42 10000 0.99  0.000000e+00 0.34434078
1243  43 10000 0.99  0.000000e+00 0.35089737
1244  44 10000 0.99  0.000000e+00 0.35738840
1245  45 10000 0.99  0.000000e+00 0.36381451
1246  46 10000 0.99  0.000000e+00 0.37017637
1247  47 10000 0.99  0.000000e+00 0.37647461
1248  48 10000 0.99  0.000000e+00 0.38270986
1249  49 10000 0.99  0.000000e+00 0.38888276
1250  50 10000 0.99  0.000000e+00 0.39499393
1251  51 10000 0.99  0.000000e+00 0.40104399
1252  52 10000 0.99  0.000000e+00 0.40703355
1253  53 10000 0.99  0.000000e+00 0.41296322
1254  54 10000 0.99  0.000000e+00 0.41883359
1255  55 10000 0.99  0.000000e+00 0.42464525
1256  56 10000 0.99  0.000000e+00 0.43039880
1257  57 10000 0.99  0.000000e+00 0.43609481
1258  58 10000 0.99  0.000000e+00 0.44173386
1259  59 10000 0.99  0.000000e+00 0.44731652
1260  60 10000 0.99  0.000000e+00 0.45284336
1261  61 10000 0.99  0.000000e+00 0.45831492
1262  62 10000 0.99  0.000000e+00 0.46373177
1263  63 10000 0.99  0.000000e+00 0.46909446
1264  64 10000 0.99  0.000000e+00 0.47440351
1265  65 10000 0.99  0.000000e+00 0.47965948
1266  66 10000 0.99  0.000000e+00 0.48486288
1267  67 10000 0.99  0.000000e+00 0.49001425
1268  68 10000 0.99  0.000000e+00 0.49511411
1269  69 10000 0.99  0.000000e+00 0.50016297
1270  70 10000 0.99  0.000000e+00 0.50516134
1271  71 10000 0.99  0.000000e+00 0.51010973
1272  72 10000 0.99  0.000000e+00 0.51500863
1273  73 10000 0.99  0.000000e+00 0.51985854
1274  74 10000 0.99  0.000000e+00 0.52465996
1275  75 10000 0.99  0.000000e+00 0.52941336
1276  76 10000 0.99  0.000000e+00 0.53411922
1277  77 10000 0.99  0.000000e+00 0.53877803
1278  78 10000 0.99  0.000000e+00 0.54339025
1279  79 10000 0.99  0.000000e+00 0.54795635
1280  80 10000 0.99  0.000000e+00 0.55247679
1281  81 10000 0.99  0.000000e+00 0.55695202
1282  82 10000 0.99  0.000000e+00 0.56138250
1283  83 10000 0.99  0.000000e+00 0.56576867
1284  84 10000 0.99  0.000000e+00 0.57011099
1285  85 10000 0.99  0.000000e+00 0.57440988
1286  86 10000 0.99  0.000000e+00 0.57866578
1287  87 10000 0.99  0.000000e+00 0.58287912
1288  88 10000 0.99  0.000000e+00 0.58705033
1289  89 10000 0.99  0.000000e+00 0.59117983
1290  90 10000 0.99  0.000000e+00 0.59526803
1291  91 10000 0.99  0.000000e+00 0.59931535
1292  92 10000 0.99  0.000000e+00 0.60332219
1293  93 10000 0.99  0.000000e+00 0.60728897
1294  94 10000 0.99  0.000000e+00 0.61121608
1295  95 10000 0.99  0.000000e+00 0.61510392
1296  96 10000 0.99  0.000000e+00 0.61895288
1297  97 10000 0.99  0.000000e+00 0.62276335
1298  98 10000 0.99  0.000000e+00 0.62653572
1299  99 10000 0.99  0.000000e+00 0.63027036
1300 100 10000 0.99  0.000000e+00 0.63396766
1301 101 10000 0.99  0.000000e+00 0.63762798
1302 102 10000 0.99  0.000000e+00 0.64125170
1303 103 10000 0.99  0.000000e+00 0.64483919
1304 104 10000 0.99  0.000000e+00 0.64839079
1305 105 10000 0.99  0.000000e+00 0.65190689
1306 106 10000 0.99  0.000000e+00 0.65538782
1307 107 10000 0.99  0.000000e+00 0.65883394
1308 108 10000 0.99  0.000000e+00 0.66224560
1309 109 10000 0.99  0.000000e+00 0.66562314
1310 110 10000 0.99  0.000000e+00 0.66896691
1311 111 10000 0.99  0.000000e+00 0.67227724
1312 112 10000 0.99  0.000000e+00 0.67555447
1313 113 10000 0.99  0.000000e+00 0.67879893
1314 114 10000 0.99  0.000000e+00 0.68201094
1315 115 10000 0.99  0.000000e+00 0.68519083
1316 116 10000 0.99  0.000000e+00 0.68833892
1317 117 10000 0.99  0.000000e+00 0.69145553
1318 118 10000 0.99  0.000000e+00 0.69454097
1319 119 10000 0.99  0.000000e+00 0.69759556
1320 120 10000 0.99  0.000000e+00 0.70061961
1321 121 10000 0.99  0.000000e+00 0.70361341
1322 122 10000 0.99  0.000000e+00 0.70657728
1323 123 10000 0.99  0.000000e+00 0.70951151
1324 124 10000 0.99  0.000000e+00 0.71241639
1325 125 10000 0.99  0.000000e+00 0.71529223
1326 126 10000 0.99  0.000000e+00 0.71813930
1327 127 10000 0.99  0.000000e+00 0.72095791
1328 128 10000 0.99  0.000000e+00 0.72374833
1329 129 10000 0.99  0.000000e+00 0.72651085
1330 130 10000 0.99  0.000000e+00 0.72924574
1331 131 10000 0.99  0.000000e+00 0.73195328
1332 132 10000 0.99  0.000000e+00 0.73463375
1333 133 10000 0.99  0.000000e+00 0.73728741
1334 134 10000 0.99  0.000000e+00 0.73991454
1335 135 10000 0.99  0.000000e+00 0.74251539
1336 136 10000 0.99  0.000000e+00 0.74509024
1337 137 10000 0.99  0.000000e+00 0.74763934
1338 138 10000 0.99  0.000000e+00 0.75016294
1339 139 10000 0.99  0.000000e+00 0.75266131
1340 140 10000 0.99  0.000000e+00 0.75513470
1341 141 10000 0.99  0.000000e+00 0.75758335
1342 142 10000 0.99  0.000000e+00 0.76000752
1343 143 10000 0.99  0.000000e+00 0.76240745
1344 144 10000 0.99  0.000000e+00 0.76478337
1345 145 10000 0.99  0.000000e+00 0.76713554
1346 146 10000 0.99  0.000000e+00 0.76946418
1347 147 10000 0.99  0.000000e+00 0.77176954
1348 148 10000 0.99  0.000000e+00 0.77405184
1349 149 10000 0.99  0.000000e+00 0.77631133
1350 150 10000 0.99  0.000000e+00 0.77854821
> 
> #################Colors Vector#################
> cols<-brewer.pal(n=3,name="Set1")
> cols[1]
[1] "#E41A1C"
> #################Quartz Code is used to save the exact figure in the Mac OS environment, for windows and other environments ignore this command##################
> ##################Figure 3##################
> quartz(width=5,height=6)
> 
> par(mfrow=c(3,1))
> ##################First panel, n=100##################
> plot(p~k,data=computation, subset=((n==100) & (q == q_1)), type="p",pch=20, col=cols[1],ylab="Probability",xlab="Number of variables",main="Lower bound on probability that all rows missing (n = 100)")
> text(y=0.5,x=25,TeX('$q_*=0.75$'))
> lines(p~k,data=computation, subset=((n==100) & (q == q_2)), type="p", pch=20,col=cols[2])
> text(y=0.5,x=58,TeX('$q_*=0.90$'))
> lines(p~k,data=computation, subset=((n==100) & (q == q_3)), type="p", pch=20,col=cols[3])
> text(y=0.2,x=100,TeX('$q_*=0.99$'))
> 
> 
> ##################Second panel, n=1,000##################
> plot(p~k,data=computation, subset=((n==1000) & (q == q_1)), type="p", pch=20,col=cols[1],ylab="Probability",xlab="Number of variables",main="Lower bound on probability that all rows missing (n = 1000)")
> text(y=0.5,x=34,TeX('$q_*=0.75$'))
> 
> lines(p~k,data=computation, subset=((n==1000) & (q == q_2)), type="p",pch=20, col=cols[2])
> text(y=0.5,x=78,TeX('$q_*=0.90$'))
> 
> lines(p~k,data=computation, subset=((n==1000) & (q == q_3)), type="p", pch=20,col=cols[3])
> text(y=0.2,x=110,TeX('$q_*=0.99$'))
> 
> ##################Third panel, n=10,000##################
> plot(p~k,data=computation, subset=((n==10000) & (q == q_1)), type="p", pch=20,col=cols[1],ylab="Probability",xlab="Number of variables",main="Lower bound on probability that all rows missing (n = 10000)")
> text(y=0.5,x=42,TeX('$q_*=0.75$'))
> 
> lines(p~k,data=computation, subset=((n==10000) & (q == q_2)), type="p", pch=20,col=cols[2])
> text(y=0.5,x=100,TeX('$q_*=0.90$'))
> 
> lines(p~k,data=computation, subset=((n==10000) & (q == q_3)), type="p", pch=20,col=cols[3])
> text(y=0.2,x=120,TeX('$q_*=0.99$'))
> 
> quartz.save("figure3.pdf", type = "pdf", device = dev.cur(), dpi = 600)
quartz 
     2 
> 
> 
> 
> ####
> 
> # Find n such that prob all units missing is .5 (or anything); solution when k allowed to be real-valued
> # (1-q^k)^(n) = 0.5
> # 1-q^k = 0.5^(1/n)
> # q^k = 1-0.5^(1/n)
> # k * log(q) = log( 1-0.5^(1/n))
> # k = log( 1-0.5^(1/n))/log(q)
> 
> ##################Computing the number of variables needed 
> computation2 <- expand.grid(n = c(100:10000),
+             q = c(q_1,q_2,q_3))
> 
> computation2$k50 <- floor(with(computation2, log( 1-0.5^(1/n))/log(q)))
> computation2$k99 <- floor(with(computation2, log( 1-0.99^(1/n))/log(q)))
> 
> ##################Displaying In-Text Numbers##################
> 
> ##################n=10,000, q_* = 0.75##################
> computation2[9901,]
         n    q k50 k99
9901 10000 0.75  33  48
> 
> ##################n=10,000, q_* = 0.99##################
> computation2[29703,]
          n    q k50  k99
29703 10000 0.99 952 1374
> 
> ##################Figure 4-1##################
> quartz(width=6,height=6)
> 
> par(mfrow=c(1,1))
> plot(k50~n,data=computation2,ylab="k",main=TeX("Largest k such that probability all data missing is $\\leq 0.50$"),col="white")
> 
> lines(k50~n,data=computation2, subset=((q == q_1)), type="p", pch=20,col=cols[1])
> text(y=5,x=9500,TeX('$q_*=0.75$'))
> 
> lines(k50~n,data=computation2, subset=((q == q_2)), type="p", pch=15,col=cols[2])
> text(y=120,x=6000,TeX('$q_*=0.90$'))
> 
> 
> lines(k50~n,data=computation2, subset=((q == q_3)), type="p", pch=20,col=cols[3])
> text(y=700,x=2000,TeX('$q_*=0.99$'))
> quartz.save("figure4-1.pdf", type = "pdf", device = dev.cur(), dpi = 600)
quartz 
     2 
> 
> 
> ##################Figure 4-2##################
> quartz(width=6,height=6)
> 
> par(mfrow=c(1,1))
> plot(k99~n,data=computation2,ylab="k",main=TeX("Largest k such that probability all data missing is $\\leq 0.99$"),col="white")
> lines(k99~n,data=computation2, subset=((q == q_2)), type="p", pch=15,col=cols[2])
> text(y=5,x=9500,TeX('$q_*=0.75$'))
> 
> lines(k99~n,data=computation2, subset=((q == q_1)), type="p", pch=20,col=cols[1])
> text(y=180,x=6000,TeX('$q_*=0.90$'))
> 
> lines(k99~n,data=computation2, subset=((q == q_3)), type="p", pch=20,col=cols[3])
> text(y=1100,x=2000,TeX('$q_*=0.99$'))
> 
> quartz.save("figure4-2.pdf", type = "pdf", device = dev.cur(), dpi = 600)
quartz 
     2 
> 
> 
> 
> ##################Figure 5##################
> quartz(width=6,height=6)
> 
> par(mfrow=c(1,1))
> plot(y~k,data=computation,subset=(n==100 & q == 0.75), type="p", ylab="Expected proportion missing", xlab="Number of Variables", ylim=c(0,1),pch=20,col = cols[1], main="Lower bound on expected proportion of data missing")
> text(y=1,x=5,TeX('$q_*=0.75$'))
> lines(y~k,data=computation,subset=(n==100 & q == 0.9),type="p",pch=20,col=cols[2])
> text(y=0.9,x=33,TeX('$q_*=0.90$'))
> lines(y~k,data=computation,subset=(n==100 & q == 0.99),type="p", pch=20,col=cols[3])
> text(y=0.55,x=100,TeX('$q_*=0.99$'))
> 
> quartz.save("figure5.pdf", type = "pdf", device = dev.cur(), dpi = 600)
quartz 
     2 
> 
> 
> proc.time()
   user  system elapsed 
 13.833   0.263  14.638 
